All EU citizens can buy a property in Austria without restriction. Non-EU citizens would need to apply for a special permit at the Land Transfer Authorities, this is a lengthy process without any guarantees that would lock the property in a sale until the permit is either granted or denied.

In a practical sense this means that sellers won’t easily accept offers from non-EU buyers. The only properties where the permit isn’t needed are designated second home or ‘zweitwohnsitz’ properties, however even here there are extra conditions that need to be met by Non-EU citizens.